New Rotary Engine Designs by Deviation Function Method - Wankel

138 Pages·2012·8.244 MB·English

by  Sarah Warren

UCLA
UCLA Electronic Theses and Dissertations
Title
New Rotary Engine Designs by Deviation Function Method
Permalink
https://escholarship.org/uc/item/2w12f40z
Author
Warren, Sarah
Publication Date
2012

Peer reviewed|Thesis/dissertation
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University of California
UNIVERSITY OF CALIFORNIA
Los Angeles
New Rotary Engine Designs by Deviation Function Method
A dissertation submitted in partial satisfaction of the
requirements for the degree of Doctor of Philosophy
in Mechanical Engineering
by
Sarah Elizabeth Warren
2012
(cid:13)c Copyright by
Sarah Elizabeth Warren
2012
ABSTRACT OF THE DISSERTATION
New Rotary Engine Designs by Deviation Function Method
by
Sarah Elizabeth Warren
Doctor of Philosophy in Mechanical Engineering
University of California, Los Angeles, 2012
Professor Daniel C. H. Yang, Chair
Conventional rotary engine designs are based on an epitrochoidal housing bore that is
foundbythepathofthepointattherotorprofile’sapex. Tosealtheengine, therotorapexes
are replaced by spring-loaded apex seals that slide along the housing bore during rotation.
The conventional designs are limited to the point-based epitrochoid housing profiles and
cannot incorporate the profile of the apex seal. This dissertation presents the complete
theory and algorithm of the deviation function (DF) method of rotary engine design. This
method is based on conjugate pair design and generates new engine profiles from generating
curves. The DF method of rotary engine design by apex seal profile is introduced and
developed for generating new profile designs in which the housing profile conforms to the
apex seal profile, for better sealing. The DF method of design by geometric parameters is
developed to select profiles using the standard rotary engine geometry. Maximum theoretical
compression ratio and swept area are two criteria that have a range of possible DF-designed
profile solutions. For the apex seal design and selection process, a sealing index is defined
and a multi-apex-sealing grid is developed to further improve apex sealing. The DF method
of rotary engine design is extended to noncircular pitch curves, for generating more new
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profiles that incorporate a variable speed ratio between the rotor and main shaft.
By using the DF method, a larger variety of engine profiles is available to meet multiple
design criteria and allow more flexibility in the design process. Some example deviation
functionsareprovidedforprocessillustrationanddesigndevelopment. Engineprofiledesigns
andmethodsusingcircularpitchcurvesaredevelopedusingbotharc-basedandnonarc-based
apex seal profiles. Engine profile designs with noncircular pitch curves are developed using
the arc-based seal profile.
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The dissertation of Sarah Elizabeth Warren is approved.
Rajit Gadh
Michael K. Stenstrom
Tsu-Chin Tsao
Daniel C. H. Yang, Committee Chair
University of California, Los Angeles
2012
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Dedicated to
Etta Warren and Dorothy Kohashi
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Contents
1 Introduction 2
2 Deviation Function Method of Rotary Engine Design 9
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Deviation Function (DF) Method . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Examples of rotary engine design . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.1 A 4th order polynomial deviation function . . . . . . . . . . . . . . . 21
2.3.2 A nonarc-based sinusoidal deviation function . . . . . . . . . . . . . . 23
2.3.3 An arc-based deviation function . . . . . . . . . . . . . . . . . . . . . 25
2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3 DF Engine Design by Apex Seal Profile 28
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Rotary Engine Design by Apex Seal Profile . . . . . . . . . . . . . . . . . . . 30
3.2.1 Design the generating curve g , the apex seal . . . . . . . . . . . . . . 30
1
3.2.2 Design the generated curve g , the engine housing . . . . . . . . . . . 34
2
3.2.3 Design the generated curve g , the rotor flank . . . . . . . . . . . . . 37
3
3.3 Examples of rotary engine design . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3.1 An arc-based deviation function . . . . . . . . . . . . . . . . . . . . . 40
3.3.2 A nonarc-based sinusoidal deviation function . . . . . . . . . . . . . . 41
3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
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4 DF Engine Design by Geometric Parameters 45
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2 Compression Ratio and Volumetric Displacement . . . . . . . . . . . . . . . 49
4.3 Deviation Functions in terms of Rotor Radius . . . . . . . . . . . . . . . . . 51
4.3.1 Arc-based deviation function . . . . . . . . . . . . . . . . . . . . . . . 51
4.3.2 Nonarc-based deviation function . . . . . . . . . . . . . . . . . . . . . 52
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5 Apex Sealing Analysis 57
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.2 Sealing Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.2.1 Apex Seal Radius of Curvature . . . . . . . . . . . . . . . . . . . . . 61
5.2.2 Housing Radius of Curvature . . . . . . . . . . . . . . . . . . . . . . 63
5.2.3 Apex Sealing Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6 Multi-Apex-Sealing Grid 68
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.2 Multi-Apex-Sealing Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.2.1 Wide Apex Seal Design . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.2.2 Multi-Apex-Seal Design . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.3 Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
7 Rotary Engine Profiles from Noncircular Pitch Curves 81
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7.2 Noncircular Pitch Curve Generation . . . . . . . . . . . . . . . . . . . . . . . 84
7.3 DF method for noncircular pitch rotary engine design . . . . . . . . . . . . . 88
7.3.1 Design the apex seal profile, g . . . . . . . . . . . . . . . . . . . . . 90
1
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7.3.2 Design the engine housing bore, g . . . . . . . . . . . . . . . . . . . 92
2
7.3.3 Design of rotor flank, g . . . . . . . . . . . . . . . . . . . . . . . . . 95
3
7.4 Arc-based Apex Seals with Noncircular Pitch Curves . . . . . . . . . . . . . 98
7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
8 Conclusions and Future Work 102
8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
8.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Appendices 104
A Rotary Engine Design Parameters 105
B Sealing Index 107
C High-Sealing Design Parameters 111
D Wide Apex Seal Design Parameters 117
Bibliography 118
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